Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in PYTHON3):

Solution:
class SegTree:
    def __init__(self, init_val, ide_ele, segfunc):
        self.n = len(init_val)
        self.num = 2**(self.n-1).bit_length()
        self.ide_ele = ide_ele
        self.segfunc = segfunc
        self.seg = [ide_ele]*2*self.num
        # set_val
        for i in range(self.n):
            self.seg[i+self.num] = init_val[i]
        # built
        for i in range(self.num-1, 0, -1):
            self.seg[i] = self.segfunc(self.seg[2*i], self.seg[2*i+1])

    def update(self, k, x):
        k += self.num
        self.seg[k] = x
        while k:
            k = k >> 1
            self.seg[k] = self.segfunc(self.seg[2*k], self.seg[2*k+1])

    def query(self, l, r):
        if r <= l:
            return self.ide_ele
        l += self.num
        r += self.num
        res = self.ide_ele
        while l < r:
            if r & 1:
                r -= 1
                res = self.segfunc(res, self.seg[r])
            if l & 1:
                res = self.segfunc(res, self.seg[l])
                l += 1
            l = l >> 1
            r = r >> 1
        return res

def segfunc(x, y):
    if x <= y:
        return x
    else:
        return y

ide_ele = 10**18

class LCA:
    def __init__(self, g, root):
        # g: adjacency list
        # root
        self.n = len(g)
        self.root = root

        s = [self.root]
        self.parent = [-1]*self.n
        self.child = [[] for _ in range(self.n)]
        visit = [-1]*self.n
        visit[self.root] = 0
        while s:
            v = s.pop()
            for u in g[v]:
                if visit[u] == -1:
                    self.parent[u] = v
                    self.child[v].append(u)
                    visit[u] = 0
                    s.append(u)

        # Euler tour
        tank = [self.root]
        self.eulerTour = []
        self.left = [0]*self.n
        self.right = [-1]*self.n
        self.depth = [-1]*self.n

        eulerNum = -1
        de = -1

        while tank:
            v = tank.pop()
            if v >= 0:
                eulerNum += 1
                self.eulerTour.append(v)
                self.left[v] = eulerNum
                self.right[v] = eulerNum
                tank.append(~v)
                de += 1
                self.depth[v] = de
                for u in self.child[v]:
                    tank.append(u)
            else:
                de -= 1
                if ~v != self.root:
                    self.eulerTour.append(self.parent[~v])
                    eulerNum += 1
                    self.right[self.parent[~v]] = eulerNum

        #A = [self.depth[e] for e in self.eulerTour]
        A = [0]*(2*self.n-1)
        for i, e in enumerate(self.eulerTour):
            A[i] = self.depth[e]*(2*self.n-1)+i
        self.seg = SegTree(A, ide_ele, segfunc)

    def getLCA(self, u, v):
        # u, v: 0-indexed
        p = min(self.left[u], self.left[v])
        q = max(self.right[u], self.left[v])+1
        m = self.seg.query(p, q)
        return self.eulerTour[m%(2*self.n-1)]

import sys
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

n = int(input())
g = [[] for i in range(n)]
for i in range(n-1):
    a, b = map(int, input().split())
    a, b = a-1, b-1
    g[a].append(b)
    g[b].append(a)

INF = 10**18
from collections import deque
def bfs(s, g):
    n = len(g)
    d = [INF]*n
    d[s] = 0
    q = deque([])
    q.append(s)
    while q:
        v = q.popleft()
        for u in g[v]:
            if d[u] == INF:
                d[u] = d[v]+1
                q.append(u)
    return d

D1 = bfs(0, g)
M = max(D1)
for i in range(n):
    if D1[i] == M:
        x = i
        break
D2 = bfs(x, g)
M = max(D2)
for i in range(n):
    if D2[i] == M:
        y = i
        break

lca = LCA(g, 0)
def dist(u, v):
    l = lca.getLCA(u, v)
    d = lca.depth[u]+lca.depth[v]-2*lca.depth[l]
    return d
d0 = dist(x,y)
res = 0
ans = []
for i in range(n):
    if i == x or i == y:
        continue
    d1 = dist(x, i)
    d2 = dist(y, i)
    temp = (d0+d1+d2)//2
    if temp > res:
        res = temp
        ans = [x+1, y+1, i+1]
print(res)
print(*ans)